High-Energy Astronomy

3.1.1 Interaction of Light with Matter

Whenever the observation of high-energy (short-wavelength) light is desired, for ex-ample from nuclear reactions, or the annihilation of electrons with positrons, the observer is confronted with two problems. First, at such wavelengths, very sophist-icated apertures must be used to infer the incident direction of the photons, because they are highly penetrating. And second, if astrophysical observations want to be made, the atmosphere of Earth hinders direct observations, as the reaction rate with atoms and molecules in the dense atmosphere is large, so that high-energy (gamma-ray) photons are eciently absorbed and down-scattered. Hence, in the case of photon energies between a few keV to several MeV, satellite-based telescopes are unavoidable.

The detection of gamma-ray photons is based on the fundamental interactions of light with matter, the photo-electric eect, the Compton-eect, and pair-production.

The lower end of the energy range is dominated by the photo-electric eect (photo-eect). If a photon is energetic enough to exceed the work function of an electron in some material, the electron is kicked out, and holds a kinetic energy which is the dierence of photon energy minus the work function. This can be interpreted as the photon being absorbed by a de-localised electron which exceeds its binding energy and leaves the material. The cross section of the photo-eect can be roughly expressed as

σ_{P E} =κZⁿ

E^m, (3.1)

whereZ is the charge number of the material which the photon is interacting with, andκis a material-dependent constant. The pair of exponents (n, m)vary from low (n = 4, m = 3) to high energies (n = 5, m = 1). This is due to the eect that at higher photon energies, also K-electrons can be ejected which is then superseding the cross section of L-, M-, ..., -electrons. The strong dependency on the atomic number Z favours high-Z materials as veto-shields for photons in this energy range.

At photon energies around 500 keV, the Compton eect is the dominant process with matter. Here, a photon is scattered inelastically on an electron causing the photon to lose energy and change its direction. This angle-dependency can furthermore be

used in Compton-telescopes. The cross section was rst derived by Klein & Nishina (1929), based also on the work of Compton who quantitatively described the change of electron energy and momentum as an impact on the photon wavelength,

λ⁰−λ= h

m_ec(1−cos(θ)), (3.2) whereθ is the scattering angle andλ⁰−λthe change in photon wavelength. In terms of energy, the scattered photon carries an energy of

E⁰ = E₀

1 + _m^E0

ec² (1−cos(θ)), (3.3) where E₀ is the incident photon energy. According to Eq. (3.3), photons can only lose energy when interacting via the Compton eect. However, the inverse Compton eect, in which an ultra-relativistic particle, for example an electron, transfers its energy to a photon, can lead to very high-energy photons. The name "inverse Compton scattering" is misleading, as the eect is still the same, but the rest frame is transformed to a relativistic particle where the photon gets Doppler-shifted to a higher energy. The angle-dependency of the Compton eect cross section is given in dierential form as

dσ_CE

dΩ (θ) = 1 2r²₀

k k₀

2 k k₀ +k₀

k −sin²(θ)

, (3.4)

where k0 = _m^E0

ec², k = _m^E0

ec², and r0 = _m^α~c

ec² is the reduced Compton wavelength.

The total cross section is then derived by integration over the solid angle (Klein &

Nishina 1929). In general, the Compton eect cross section is a linear monotonically decreasing function of Z.

As already described in detail in Sec. 2.2.4.2, electron-positron pair-production be-comes possible above photon energies of2m_ec², and dominates by far over the other interaction processes at very large energies. The pair-production cross section has been shown to increase monotonically with energy, and shows in general a Z² de-pendence, cf. Eq. (2.21).

3.1.2 Gamma-Ray Detectors

In many applications, the scintillation method is used to detect gamma-rays by their interactions with matter. In this technique, the excitation of an electron, induced from the photon interaction, from the valence band into the conduction band is used.

The resulting electron-hole pair will recombine after a certain time, yielding another but lower energy photon. If, for example, a pure crystal is used for scintillation, the secondary photons may have wavelengths outside the visible band. The light output of a pure crystal is also very low, because the recombination processes are

inecient. If crystals are doped, which means integrating chosen impurities, there will be additional levels between the valence and the conduction band, making the excitation more probable (Hofstadter 1948). Then, the produced photons from a doped crystal are in the wavelength range 250-650 nm, which makes them usable in photomultiplier tubes or photodiodes. The optical signal which results from one gamma-ray photon is very weak. It has to be transferred into a measurable electronic signal via the amplication of photomultiplier tubes or photodiodes.

Figure 3.1: Interaction strengths of photons with Ge as a function of energy. Shown is the fraction of full-peak energy contributed by dierent energy loss mechanism in a6 cm×6 cmhigh-purity Ge detector. Photo-electric absorption is dominating below photon energies of≈140 keV. Above this energy, single and multiple Compton-scattering increases the Compton continuum as shown in Fig. 3.2b. In the energy range of the gamma-ray spectrometer SPI (<8 MeV, Sec. 3.2.2), pair-production contributes signicantly only above 3 MeV. From Roth et al. (1984).

In order to detect gamma-rays, a detector in space must meet the following criteria:

The material should have a high enough density for the photons to maximise the cross section for interaction, but at the same time may not be too heavy to lift. Addi-tionally, the light yield should be large enough. In general, organic scintillators have low densities and low light outputs, which makes them not too suitable gamma-ray detectors. Nevertheless, they are used in astrophysics because of their fast response times. For this reason, they are often a favoured choice as anticoincidence shields (Lichti & Georgii 2001). Among the most commonly used inorganic scintillators are NaI(Tl), CsI(Tl), and Bi₄(GeO₄)₃ (BGO). BGO has one of the largest densities of scintillator materials, and thus a large stopping power, but the light yield is rather low. It is often used in combination with gamma-ray detectors as anticoincidence shield material. In order to measure high-resolution gamma-ray spectra, scintillat-ors are not the best choice, as most of them have relatively large band gaps of the order 5-9 eV. The creation of electron-hole pairs is then hindered, and the energy resolution is limited by statistical uctuations to about 10%. Semi-conductors like Si or Ge have small band gaps (Si 1.12 eV, Ge 0.67 eV at room temperature) com-pared to scintillators, which increases the number of charge carriers for one incident

photon by about two orders of magnitude, resulting in an improvement of spectral resolution of at least one order of magnitude. Furthermore, Ge also has a high density of 5.33 g cm⁻³, so that the interaction probability is large, even for small-sized detectors. A physical signal out of one impinging photon is then created by applying a high voltage of typically 2-9 kV across the detector, meaning between the outer surface and an inner hole. A gamma-ray photon is mainly absorbed in the outer most parts of the detector, creating a secondary electron. This electron is then creating electrons and holes, whose numbers are proportional to the energy of the incident photon. The holes are trapped easily on their way to the cathode. For this reason, an n-type detector is created by doping Li to the Ge lattice to make the holes' paths as short as possible. Although the small band gap of Ge provides best high-resolution gamma-ray spectra, the number of thermal excitations of electron-hole pairs is non-negligible even at room temperature. Consequently, high-purity Ge detectors are cooled down to≈100 K in order to avoid disturbing leakage currents.

Moreover, solid-state detectors are very sensitive to radiation damage which worsens the resolution, and even changes the instrumental response function over time.

In this work, the spectrometer telescope SPI aboard the satellite INTEGRAL (see Sec. 3.2.1), is used for data analysis. The SPI camera consists of 19 high-purity Ge detectors, surrounded by an anticoincidence shield made of BGO, and a plastic scintillator. The dierent interaction strengths of photons with a Ge detector are shown in Fig. 3.1. When a gamma-ray spectrometer like SPI is recording photon spectra, the incident spectrum is suering from the dierent interactions of light with matter, at dierent relative strength for dierent energies. An ideal detector would translate an arbitrary shaped spectrum to the spectrum itself, but a real detector features spectral responses according to the properties of the photon and the detector. In general, a measured spectrumD(E)is described by a convolution of the incident, true source spectrumS(E)with the spectral response functionR(E),

D(E) =S(E)⊗R(E)≡ Z +∞

−∞

S(E⁰)·R(E+E⁰)dE⁰, (3.5) which can be seen as a blurring eect of the sharply dened source spectrum. In the case of Ge detectors, the spectral response is composed of a photo-peak, a Compton continuum, and escape peaks. The interaction of an incident mono-energetic beam of photons via the photo-eect leads to the photo-peak at exactly the energy of the photon, but blurred by the instrumental resolution, given by charge carrier statistics.

In the case of Compton scattering in the detector, a continuum of energies can be transferred to the charge carriers, ranging from zero (θ = 0) to the maximum (θ =π) predicted energy E_e^max− as derived from Eq. (3.3),

E_e^max− = E₀−E⁰|_θ=π =E₀ 2_m^E0

ec²

1 + 2_m^E0

ec²

!

. (3.6)

The gap between the photo-peak and the maximum Compton recoil electron energy, E_C, is hence given by

E_C ≡E₀−E_e^max− = E₀ 1 + 2_m^E0

ec²

, (3.7)

which reduces to E_C ≈ ¹₂m_ec² in the case of high-energy photons (E₀ m_ec²). In the case of pair-production in the intense electric eld of a Ge detector lattice, the incident photon of at least 1.022 MeV energy converts to an electron and a positron with masses of 511 keV c⁻² each, and kinetic energies corresponding to the energy of the photon, so that

E_e⁻+E_e⁺ =E₀+ 2m_ec². (3.8) The electron and the positron are slowed down after only a few millimetres in the detector, and deposit their kinetic energies. As their rest masses are not transferred, an additional spectral line at an energy of E₀−nm_ec² is produced in the measured spectrum. When both, electron and positron, have deposited all their kinetic energy to the detector, a double escape peak withn= 2 appears. Once the positron slowed down to thermal energies, it will annihilate or combine with a normal electron in the lattice. This corresponds to the disappearance of both particles, and a conversion to two 511 keV photons, virtually at the same time as the incident photon arrived.

If one of the 511 keV photons again interacts with the Ge detector, and one leaves the system, a single escape peak with n= 1 is measured. In Fig. 3.2a, the possible interactions of high-energy photons with a Ge detector is shown, together with the expected spectrum in the case ofE₀ 2m_ec² in Fig. 3.2b.

(a) Photon interactions in the volume of a detector. (b) Resulting spectral features.

Figure 3.2: Photon interactions and spectral response of a germanium detector. From Knoll (2010).

3.1.3 Gamma-Ray Telescopes

Solid-state detectors provide a good energy resolution, but have intrinsically no information about the direction a photon came from. With a spark chamber or a Cherenkov detector, for example, the direction of an incident gamma-ray photon can be measured well, but the energy information and spectral resolution is very restricted. In general, there are many ways to make a gamma-ray telescope out of a gamma-ray detector but since the SPI telescope, which features a Ge detector

camera, is used for the analysis in this thesis, the coded-mask principle and aperture is worked out.

(a) A coded mask illuminated by an idealised source and its associ-ated point source response func-tion. From Skinner (2004).

(b) A schematic diagram illustrating the working principle of a coded aperture:

the recorded count rate in each pixel of the detector plane is the sum of contributions from each source ux modulated by the mask. In particular the shadows generated by two sources at innite distance from the mask-detector system, one on axis and the other at the edge of the eld of view are shown. From Caroli et al. (1987).

Figure 3.3: The function principle of a coded-mask system.

Whenever a coded-mask system is used, a position-sensitive camera has be to con-structed, for example by arranging many Ge detectors in an array. The working principle of such a system is illustrated in Figs. 3.3a and b, in which a point source, located at innity, is illuminating a mask, consisting of transparent and opaque ele-ments. The mask is situated above the detecting array and transforms the "beam"

of photons into a certain shadow pattern (shadowgram), depending on the aspect angle of source and telescope. These known shadowgrams from dierent directions are then used to reconstruct the position of sources in the eld of view of the tele-scope as dened in Fig. 3.4. For point-sources, this reconstruction is mostly unique, but for diuse celestial emission, a coded-mask telescope must rely on morphology gradients, as otherwise the mask pattern is identical from all directions.

In general, the reconstruction is better the more pixels there are in the detector array.

However, the smaller the detector size, the less ecient will high-energy photons in the MeV range be detected. The apertures of coded-mask systems have a relatively large "fully coded eld of view", because the mask plane is often more extended than the detector plane. Only the geometry of the instrument is responsible for the eld of view, which is typically in the range of tens of degrees. Also the angular resolution, ∆θ, is only determined by the separation between detector array and maskl, the characteristic size of transparent elementsm, and the characteristic size of opaque elements d, to (Skinner 2008)

Figure 3.4: Field of view denition of coded-mask telescopes. The fully coded eld of view (FCFOV) is dened as comprising all directions for which the recorded ux is entirely modulated by the mask and the partially coded eld of view (PCFOV) for which only a fraction of the detected ux is coded by the mask. From Caroli et al. (1987).

∆θ= s

m l

2

+ d

l 2

. (3.9)

In fact, it is most ecient to construct a coded-mask instrument for which the transparent and opaque elements have the same size (Skinner 2008), so that the angular resolution is only depends on the ratio d/l. Decreasing the pixel elements is similar to constructing a pinhole camera but suers from detection eciency.

Increasing the separation between mask and detector ("focal length") is only possible as far as the instrument ts on a satellite to be launched into space. Typically, the angular resolution of MeV coded-mask telescopes is thus of the order of degrees.

In order to resolve ambiguities on the detector plane, due to the fact that there are more "sky pixels" than "detector pixels", the instruments are "dithered" from pointing to pointing around the object in the sky, so that there will be also temporal coding in addition to the spatial coding of the mask. The specications of the SPI instrument will be discussed further in Sec. 3.2.2.

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